Separation of CT Nominal-Actual Comparisons for Compensation of Plastic Injection Molds

Transcription

1 Separation of CT Nominal-Actual Comparisons for Compensation of Plastic Injection Molds Robert Schmitt 1, Christopher Isenberg 1 1 WZL of RWTH Aachen University, Steinbachstr. 19, Aachen, Germany, C.Isenberg@wzl.rwth-aachen.de Abstract The whole process from the first sample to the production release in injection molding is expensive and time consuming. The X-ray computed tomography (CT) enables to measure inner and outer work piece geometries holisticly and non-destructively with a very high point density. When it comes to a large amount of features the CT is a time efficient measurement method. CT typical nominal-actual comparison show the total form deviation consisting of a superposition of deviations of different orders, namely position, form, waviness and roughness (DIN 4760). The interpretation and function oriented inference from CAD-to-part comparison on the tool compensation process is not standardized. The tool compensation process could be improved by knowing the form deviation orders. In this paper a separation software and the mathematical approach for separating the total form deviation into different form deviation orders by fitting order related multidimensional curves are presented. A method of how to use separation results for mold compensation is proposed. Keywords: CT, plastic injection molding, mold compensation, CAD-to-part comparison, form deviation, separation 1 Compensation of plastic injection molds Plastic injection molding is one of the most important production processes. It enables the production of highly complex parts (e.g. connectors) in high quantities at reasonable prices. [1,2] The quality of the parts is influenced directly by the quality of the mold. [3] In addition, the injection molding process (e.g. material, packaging pressure, cooling time, mold alignment) itself has a significant influence on part quality. Although, there are different methods available to optimize the mold design and the production process (e.g. flow simulations, design of experiments), it remains difficult to predict the final quality of the produced part. [4,5,6] The final compensation has to be done on the mold. Since the quality of the part must be assured, the steps from part design to production release often require several time consuming iterations. Figure 1 shows a model of a product development work flow starting at the input of part data (CAD), followed by mold design and manufacturing, process parameter setup, mold optimization and finally production start. Once an optimal injection molding process is established, samples are produced and consequently measured. If the parts do not fit the geometric requirements, specialists deduct actions by interpreting measurement results. The interpretation and the transfer to mold compensation depends significantly on the experience of the specialists. The measurements of plastic injection molded parts are still mainly done by optical and tactile measurement procedures. For complex, feature rich parts (e.g. connectors) the measurements require a lot of time. Inaccessible features must be made accessible by slicing the part, which can alter or even destroy features. The whole process from the first sample to the production release is often expensive and time-consuming since it depends a lot on experience, trial and error and not on an objective methodology. ict Conference

2 Figure 1. Model of a product development work flow X-ray computed tomography (CT) can significantly improve the mold optimization process. The CT is capable of measuring inner and outer work piece geometries holistically and non-destructively with a very high point density. [7] When it comes to a large amount of features, the CT is an accurate and time efficient measurement method. The CT nominal-actual (CAD-to-part) comparison is a colorcoded deviation presentation of the topography of the measured (actual) part and the nominal geometry of the CAD model. The nominal-actual comparison represents the total form deviation of the entire part. Figure 2 shows an optimization loop for mold optimization using the CT measurement data for mold compensation. A part is produced and consequently measured on the CT. The nominal-actual comparison reveals the deviations. However, the interpretation from nominal-actual comparison on the mold compensation process is challenging and requires a specialist who creates correction values. The mold optimization could be significantly improved by a better exploitation of the information contained in the nominal-actual comparison. The total form deviation can be interpreted as a superposition of deviations of different orders, namely position, form, waviness and roughness according to DIN 4760 (see figure 3). A separation into different deviation orders could help on the one hand to relate specific deviations to process parameters and on the other hand to obtain a mathematical description of the specific shape of the deviations. Figure 2. Mold optimization loop 448

3 2 Separation Approach The separation approach for the current work was adapted from a work of Pfeifer et al. [8]. In this chapter the separation calculations are outlined. Figure 3 - Global forms and residuals from deviations separation The deviations between a nominal and actual surface can be considered as a superposition of different form deviations orders as illustrated in Figure 3. The separation calculations for each order can be done by best-fit approximation and least square method by minimizing the sum of the squares of the residual deviations and the best-fit function for each order. The objective function is given by: The 0 th order form deviations represent a positional offset. The best-fit function for this order is given by: s x, y z The calculation is performed directly on the deviations between nominal and actual surfaces. δ δ The 1 st order form deviations are considered as a plane which represents an inclination of the global topography. The equation of a plane is given by: 0 In this case the domain is a set of pairs (x,y). Thus, the best-fit function s for this order can be written as:, The calculation is performed on the residuals:, ict Conference

4 The 2 nd order form deviations can be interpreted as the curvature and anisotropy of the global topography. The second order surface can be expressed in the matrix notation by:, 0 Where the matrices and are given by:, 1 1 The second order surfaces are the points that satisfy the equation s(x)=0 when rank(a)=0. The second order surface expressed in matrix notation is a quadratic form and A is a real symmetric matrix. An arbitrary surface can be obtained from the proper forms by applying a suitable rotation R, parallel translation Q and scaling transformation S matrixes. Where the matrixes R, Q and S are given by: , cos, sin sin cos Although there are five fundamental forms we can reduce them, due to the application purpose, into two types: a paraboloid and an ellipsoid/hyperboloid function. The paraboloid function is used as bestfit function for the second order. The paraboloid is sufficient to evaluate the curvature and the anisotropy of the second order. In addition, it has more stability and is more time saving, since only 6 parameters need to be calculated (instead of 7 as in the case ellipsoid/hyperboloid function). [8] The paraboloid equation is given by: After applying the rotation, parallel translation and scaling transformation the equation can be written by:, cos sin sin cos In contrast with the first and zero order, the second order form cannot be solved analytically. For a good approximation the quasi-newton method can be used with initial values chosen so that: 1, 1 The calculation is performed on the residuals: 0, Xlength, Ylength,, 450

5 3 Software Implementation This chapter introduces the software prototype. Figure 4 shows a schematic of the software. Figure 4. Software main block functions schematic The user interface (figure 5) allows the user to select a nominal file (CAD model) and an actual file (point cloud). The CAD model filetype is a standard STL ASCII. The point cloud contains actual points in xyz coordinates obtained from a CT measurement. The software can handle: STL ASCII file (.stl), text file (.txt), spreadsheet file (.xlsx). The data must be aligned in order to proceed with the surface deviations calculation. If necessary, the data can be best-fitted using the Best-Fit Data button that executes an ICP algorithm [9,10]. Figure 5. Main window of the SmartInspeCT software The user selects a surface from the model by clicking with the data cursor in the desired surface. The software calculates the closest surface from the data cursor position and highlights it. The mesh segmentation is done by a region growing algorithm. It segments surfaces with respect to continuity in their normals. In order to separate planes from rounds a filter checks the surface orientation and filters the elements that present their orientation (normal vector) in a specific direction. The surface deviations (nominal-actual comparison) are calculated at each point of the nominal surface. The norm of the vector that connects the point in consideration and its closest point of the point cloud are calculated using a nearest neighbor method [11]. Then, the projection at the normal direction of the point is calculated. Therefore, a normal approximation of the nominal surface points ict Conference

6 and a certain amount of sampling points from the nominal surface with their respective deviation are required. A surface enrichment method adds triangles to the current surface in order to increase the density of its information. The implemented method sums the normals of the triangles that share a certain vertex and then normalizes the sum to produce the vertex normal. [12] The deviation separation mathematics are outlined in chapter 2. The lsqcurvefit function from the Mathworks Matlab optimization toolbox 4.2 solves the best fit function of each order. [13] The result visualization in figure 6 shows the results of a separation performed on the marked surface of the plastic connector in figure 4. The measurement was done on a Zeiss Metrotom For the alignment and the export of CAD mesh and point cloud Zeiss Calypso 5.4. was used. The screen in figure 6 is divided in 4 frames. The first frame visualizes the selected nominal and actual surfaces. Frame 2 shows the best fit surfaces and visualizes the form/shape. Frame 3 displays all parameter values with their correspondent unit. In addition, the RMS values of each order are characteristic values for the relevance of each order on the total deviations. Frame 4 shows a direct comparison between the nominal surface and the nominal surface plus the deviation form and also between the nominal and the residuals of the correspondent order. Figure 6. Results view of SmartInspeCT software The software saves every single surface plus the sum of 0, 1 st, and 2 nd orders are saved as stl files. The new window button opens separate figures for a more detailed visualization. The software was developed in Mathworks Matlab 2011a. 452

7 4 Mold Compensation The CT is already used as a measurement technique for inspection of plastic parts. The mold compensation is still based on measurements of single points. The engineer derives compensation values from the dimensional deviation of the measured points (Figure 7). Based on these values compensating surfaces are created in the CAD environment. Since only few points are used, the surface deviations are not entirely covered by the compensating element. The results depend on the experience of the engineer and on position and amount of measurement points. Various time consuming iterations of the loop shown in Figure 2 could be required. Figure 7. Single measurement points on CT model for mold compensation The separation approach could significantly improve and speed up this process. The sample will be measured with CT. Once the alignment of nominal and actual data and the data export (point cloud and stl) are completed, the surfaces of the part will be analysed with the SmartInspeCT software. The software provides a surface composed of the sum of the deviation order surfaces. This surface approximates the real surface using basic shapes. Reverse engineering software can be used to reconstruct the surface and save it in CAD format. Figure 8 shows a wire model of the connector and the reconstructed surface of the SmartInspeCT software. Figure 8. Wire model of the connector with reconstructed surface from SmartInspeCT ict Conference

8 It is the same surface as shown in Figure 7. Subsequently, the surface is transformed to the compensating surface by creating a negative (mirrored at the nominal surface). Adapted eroding tools can be designed to manufacture the compensated mold. 5 Summary In this work we presented a software to separate CT nominal-actual comparisons into different form deviation orders. The mathematics of the separation approach were outlined. A method for using the separation results for mold compensation was proposed. Acknowledgements The present work is part of the project SmartInspeCT Separation of nominal-actual comparisons to improve processes in tool and mold manufacturing. Within this project WZL cooperates with BOIDA Kunststofftechnik GmbH & Co. KG, Proplas GmbH and the associated partner Carl Zeiss IMT. This research and development project was funded by the German Federal Ministry of Education and Research (BMBF) within the Funding Action SME Innovative: Research for Production (02PK2226) and managed by the Project Management Agency Karlsruhe (PTKA). The author is responsible for the contents of this publication. References [1] Schmitt R, Doerner D (2006) Measurement Technology for the Machine-Integrated Determination of form Deviations in Optical Surfaces. Annals of the CIRP 55(1): [2] Nakao M, Yoda M, Nagao T (2003) Locally Controlling Heat Flux for Preventing Micrometre- Order Deformation with Injection Molding of Miniature Products.Annals of the CIRP 52(1): [3] Altan T, Lilly B, Yen Y C (2001) Manufacturing of Dies and Molds. CIRP Annals Manufacturing Technologies 50(2): [4] Chen Z, Turng L (2005) A Review of Current Developments in Process and Quality Control for Injection Molding. Advances in Polymer Technology, Vol. 24, No. 3, [5] Chang R, Yang W (2000) Numerical simulation of mold filling in ijection molding using a three dimensional finite volume approach. Int. J. Numer. Meth. Fluids, 37: [6] Postawa P, Koszkul J (2005) Journal of Materials Processing Technology : [7] Kruth JP, et al. (2011) Computed tomography for dimensional metrology, CIRP Annals 60(2): [8] Pfeifer T, Kurokawa S, Meyer S (2001) Derivation of parameter of global form deviations for 3-dimensional surfaces in actual manufacturing processes. Measurement, Vol.29, pp [9] Besl P, McKay N (1992) A Method for Registration of 3-D Shapes. IEEE Trans. Pattern Analysis and Machine Intelligence, pp [10] Gelfand N, Ikemoto I, Rusinkiewicz S, Levoy M (2003) Geometrically stable sampling for the ICP algorithm. Proc. 4th International Conference on 3D Imaging and Modeling (3DIM), pp [11] Arya S, Mount DM, Netanyahu NS, Silverman R, Wu A (1998) An optimal algorithm for approximate nearest neighbor searching. Journal of the ACM 45(6), [12] Eberly D (2008) Mesh differential geometry. Geometric Tools, LLC [13] The MathWorks (2009) Optimization Toolbox ( ) 454